What the next two patterns of -12,60, -300,1500

The given sequence is: 

\[
-12, 60, -300, 1500, \dots
\]

To find the next two terms, let's investigate the pattern. Notice that each term alternates in sign, suggesting multiplication by a negative factor. Let's check the ratio between consecutive terms:

1. \(\frac{60}{-12} = -5\)
2. \(\frac{-300}{60} = -5\)
3. \(\frac{1500}{-300} = -5\)

Each term is multiplied by \(-5\) to get the next term. 

Therefore, the next terms in the sequence can be found by continuing this pattern:

- \(1500 \times -5 = -7500\)
- \(-7500 \times -5 = 37500\)

Thus, the next two terms are:
\[
-7500, 37500
\]

Would you like a deeper explanation on how to identify such patterns or explore related sequences?

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Here are five questions to expand on the topic:

1. Can you identify other common types of sequences and patterns (like arithmetic or geometric)?
2. What is the difference between linear and exponential sequences?
3. How would you determine if a sequence is quadratic?
4. Can you write a general formula for the nth term of this sequence?
5. What is the importance of recognizing patterns in real-world problems?

**Tip**: Always check the ratio or difference between terms when identifying patterns—it helps in distinguishing between arithmetic, geometric, or more complex sequences.

What are the next two patterns of -12, 60, -300, 1500?

Discover the next two terms of the geometric sequence: -12, 60, -300, 1500. Learn how to recognize and solve patterns in a geometric progression by using the common ratio formula. Suitable for students in Grades 6-8.

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